This application is based upon and claims the benefit of priority from the prior Japanese Patent Applications No. 11-328333, filed Nov. 18, 1999; and No. 2000-344273, filed Nov. 10, 2000, the entire contents of which are incorporated herein by reference.
The present invention relates to a method for quantum information processing using a solid-state element, and more particularly to relates a method for quantum information processing in which operation is optically performed and which can attain high scalability of quantum bits (qubits) and to a quantum information processor.
A new information processing method is proposed for performing information processing in quantum processes in which quantum states of an atom such as a ground state and an excited state are set so as to correspond to xe2x80x9c0xe2x80x9d and xe2x80x9c1xe2x80x9d and bits are expressed by using each quantum state |0 greater than  or |1 greater than  or a superposition state xcex1|0 greater than +xcex2|1 greater than  their of (where xcex1 and xcex2 are complex numbers). Quantum computers based on such quantum information processing are proposed and formulated by Bennioff (P. Bennioff, Phys. Rev. Lett., 48, 1581 (1992)), Feynman (R. P. Feynman, Found. Phys., 16, 507 (1986)), and Deutsch (Proc. Roy. Soc. London, Ser. A400, 96 (1985)), and are now popularly studied.
In a conventional computer (a classical computer), a bit carrying information takes a value of xe2x80x9c0xe2x80x9d or xe2x80x9c1xe2x80x9d. On the contrary, a bit in the quantum computation can take a value of not only |0 greater than  or |1 greater than  but also their superposition state xcex1|0 greater than +xcex2|1 greater than . Such a bit is called a quantum bit (qubit). In the quantum computation, a plurality of (N) qubits is simultaneously dealt with and the whole qubits are subjected to unitary transformation called a gate operation to perform computation. Since the N qubits simultaneously express 2N numbers, it becomes possible to make 2N parallel computations. Therefore, it is possible to make extremely rapid computations for a certain problem.
Thus, the quantum computer has a potential capacity exceeding that of the classical computer in quality and is expected as the future information processing technology and computing technology. However, it has been considered that it is extremely difficult to realize the quantum computer. This is because it is difficult in practice to retain the superposition quantum states during computations and prevent a change other than the intended change of states by the gate operation from occurring. Further, in the quantum computation, it is necessary to couple the qubits to each other with retaining quantum coherency, but this is also difficult.
However, so far, some physical systems which make it possible to realize the quantum computation are proposed, and recently, some experiments are demonstrated.
One example is a method using ion trap that is theoretically proposed by Cirac and Zoller (J. I. Cirac and P. Zoller, Phys. Rev. Lett., 74, 4091 (1995)). In this method, individual ions are separated from one another by a distance of the order of micrometer or more and held in an electromagnetic trap at extremely low temperatures, and electron excited levels and a collective vibrational level of the ions are used. The collective vibrational level is a vibrational excited state related to the center-of-mass motion of all of the ions and serves to couple individual ions, i.e., qubits. An independent ion in the trap is hard to receive unnecessary interaction from the external world, and can retain the superposition state for a long period of time, which is a major premise for the quantum computation. However, it is necessary to use a large-scale apparatus for the ion trap at extremely low temperatures and thus it is difficult to reduce the size of the element. Further, the qubit is distinguished based on the position of the ion and a spatially converged laser beam is irradiated to aim at the specified ion. Thus, since the processing operation is effected with the individual qubits distinguished from one another by selectively applying the laser beam to the specified ion, it is necessary to separate the ions by a distance of at least approximately the wavelength of light, and therefore the integration of the elements and the scalability of the qubits are restricted.
Proposal of an NMR quantum computer using a nuclear spin of an atom in a molecule as a qubit is known as another physical system which can be experimented (N. A. Gershenfeld, I. Chuang, Science, 275, 350 (1997)). In this method, a magnetic field is applied to molecules in a solution, thereby allowing energy levels of the nuclear spin to cause Zeeman splitting. Then, the computation is executed by operating the quantum state of the nuclear spin, i.e., the qubit by affecting a high-frequency electromagnetic field resonant with the split energy level. The degree of the Zeeman splitting is different depending on the types of atoms and also different depending on the position of the atom in the molecule even if the atoms are of the same type. Therefore, it becomes possible to select a nuclear spin resonant with the frequency of the high-frequency electromagnetic field and to operate a single qubit. In the NMR quantum computer, the computation up to three bits is demonstrated. However, in this method, since each molecule acts as one computer, there occurs a problem that the number of qubits cannot be freely increased.
The above two examples are most advanced researches at present in which experiments for a quantum gate operation and execution of a simple computation algorithm are performed. However, as described above, for practical computation, a problem occurs in the scalability of the qubits. Further, in the above examples, a single ion in a trap or a nuclear spin of a molecule in a solution is used as a qubit. However, it is desired to make quantum computation by use of solid-state qubits that can be easily dealt with and have an advantage in reduction in size and integration.
As a study for realizing the quantum computation using a solid-state element, an experiment of a qubit using a Josephson junction is known (Y. Nakamura, Yu. A. Paskin and J. S. Tsai, Nature, 398, 786 (1999)). Nakamura et al. have succeeded in creating a superposition state of two states different in the number of electrons by use of microelectrodes in superconductive states. However, in this case, an advanced fine fabricating process is required for formation of qubits and coupling between a plurality of qubits. Further, an effective method for coupling coherently a large number of qubits is not known.
In addition, it is proposed a method for executing a quantum computation in which a metal atom or a molecule is held in fullerene and the electron states of a xcfx80 electron of the fullerene are utilized as qubits (Fukumi et al., Jpn. Pat. Appln. KOKAI Publication No. 10-254569). In this method, the phenomenon is utilized that light frequencies for exciting the xcfx80 electron of respective fullerene molecules are different depending on the number of carbon atoms in the fullerene or the type of the metal atom or the molecule, and fullerene used as a qubit is selected according to the wavelength of irradiated light to perform a processing operation. In this method, the qubits are coupled by bonding the fullerene molecules with an organic cross-linking molecule. In other words, an artificial xe2x80x9cmoleculexe2x80x9d, in which the fullerene serves as an atom and the organic cross-linking molecule serves as the interatomic bond, is used instead of the molecule in the NMR computer. However, since a highly fine fabricating technology or synthesis process is required for coupling qubits in this method, it is considered difficult to attain scalability to a large number of qubits. Further, since two levels of the ground state and the excited state of the xcfx80 electron coupled through an allowed transition are utilized for a qubit, decoherence by relaxation is easily caused, and therefore difficulty is expected in retaining the superposition state for a sufficiently long time necessary for computation.
As described above, in a physical system such as a single ion in a trap or a molecule in a solution, it is possible to retain coherency for a long period of time and a simple gate operation has already been realized. However, the above physical systems are hard to handle compared with the solid substance and also have difficulty in reduction in size and integration as elements, and further the scalability of the qubits is low. On the other hand, in the solid-state element, since decoherence is rapidly caused because of the method for operating the qubits and a material constituting the qubits, it is difficult to maintain the superposition state. Further, it is necessary to couple qubits by use of a substance in the real space in the solid-state element, which requires an extremely fine fabricating technique and brings about difficulty in coupling a large number of qubits.
Under the above circumstances, conventionally, it is difficult to realize an element or an apparatus for quantum information processing, for example, a quantum computer.
An object of the present invention is to provide a method for quantum information processing and a quantum information processor that is compact and practical and uses a large number of qubits, that can retain the superposition state for a sufficiently long decoherence time and that is almost free from decoherence other than intended change of states during the gate operation without requiring a difficult fine patterning process, chemical synthesis and a wiring by a crystal growth process.
A method for quantum information processing according to the present invention comprises:
providing physical systems arranged in a resonator, each physical system having three energy levels, two transitions of three transitions between the three levels being optically allowed, wherein a quantum bit of each physical system is expressed by either of quantum states of two levels constituting a remaining optically forbidden transition or by their superposition state, and wherein at least two physical systems are included, one transition of the optically allowed two transitions being different in transition frequency for respective physical systems, and the at least two physical systems being coupled quantum-mechanically through a common resonator mode;
irradiating one physical system selectively with two kinds of light, frequency difference thereof corresponding to a transition frequency of the optically forbidden transition of the physical system, thereby setting an initial state;
irradiating the other physical system selectively with two kinds of light, frequency difference thereof corresponding to a transition frequency of the optically forbidden transition of the other physical system, thereby setting an initial state; and
irradiating the two physical systems simultaneously with two kinds of light, the two kinds of light having frequencies resonant with the optically allowed transitions other than the transitions coupled through the common resonator mode, while increasing an intensity level of one of the two kinds of light and decreasing an intensity level of the other light between start time and finish time of the simultaneous irradiation, thereby exchanging the quantum states between the two physical systems.
In the method of the present invention, since the superposition state of the two levels, the transition between them being optically forbidden, are used as a qubit expressing information, decoherence caused by relaxation can be alleviated. In addition, since a technique referred to as adiabatic passage can be applied that enables to cause a change of superposition state of the lower two levels without excitation to the upper level for operating the qubit with utilizing two kinds of light, decoherence caused by relaxation from the upper level can be alleviated during a gate operation. Further, since a qubit to be operated is selected from physical systems coupled through a resonator mode according to the frequency of light, a large number of qubits can be integrated in a space of a wavelength order.
In the method of the present invention, atoms, ions, molecules or the like held in a solid substance can be used as physical systems. One transition of optically allowed two transitions is different in transition frequency for respective physical systems according to a surrounding local field such as a magnetic field and an electric field. For example, ions contained in a solid substance are used as physical systems and neighboring two levels generated by hyperfine structure splitting caused by a nuclear spin of each ion can be used as the above two energy levels. The solid physical system can be easily formed into an element.
In the method of the present invention, the physical systems are divided into a plurality of physical system groups each of which includes a plurality of physical systems whose transition frequencies are in a given range and the quantum states of the plurality of physical systems contained in each group may be collectively changed. In this case, since the plurality of physical systems expresses one qubit, a large read-out signal can be obtained and occurrence of an error can be suppressed.
In the method of the present invention, the physical systems are arranged in a resonator and the physical systems are quantum-mechanically coupled through a common resonator mode. In this case, the qubits can be coupled irrespective of the position of the physical systems in the solid substance. Therefore, it is unnecessary to use a difficult superfine process technique and also to form wires. The resonator may be provided outside the solid substance holding the physical systems. The resonator may be constituted by polishing the opposite surfaces of the solid substance. It is more preferable to constitute the resonator by forming multi-layered coatings on the opposite surfaces of the solid substance. The resonator formed of the multi-layered coatings is small and can enhance the coupling effect of the qubits. Further, in the present invention, it is possible to use a spherical or disk-like solid substance, to form a multi-layered coating on the curved surface thereof and to confine light inside the solid substance by total reflection.
In the present invention, the physical systems may be applied with a magnetic field or an electric field together with irradiation with light to utilize levels subjected to splitting by breaking degeneracy of the two levels constituting the optically forbidden transition. In this case, since the quantum states are retained with utilizing respective levels split by breaking degeneracy, the degree of freedom for quantum information processing can be improved.
In the method of quantum information processing according to the present invention, a computation is executed by combining changes of quantum states of a plurality of physical systems. For example, a computation can be executed by combining a controlled-NOT operation of two qubits and a one-qubit operation.
In the case of performing the one-qubit operation, two kinds of light that resonate with optically allowed two transitions of the physical system intended to change the quantum state may be selected. Alternatively, in the case of performing the one-qubit operation, it is preferably to select two kinds of light that do not resonate with any of optically allowed two transitions but two-photon resonate with a remaining optically forbidden transition. When the two kinds of light that two-photon resonate with the optically forbidden transition are selected, even if physical systems other than the physical system intended to perform the gate operation are present in levels resonant with the resonator mode, the gate operation can be performed without affecting such physical systems or qubits consisting of the physical systems other than a desired qubit.
In the present invention, in order to suppress influence of physical systems not utilized as qubits to the qubit to be operated, a preprocessing operation may be performed prior to the controlled-NOT operation to change the physical systems into the specific states by irradiating the physical systems with light having a frequency resonant with the optically allowed transitions while scanning the frequency thereof. In this case, assuming that a scanning range of a light frequency irradiated for the preprocessing is xcex94xcexdBw, a central transition frequency of the |0 greater than xe2x88x92|1 greater than  transitions is xcexd01center, and an inhomogeneous width of the |0 greater than xe2x88x92|1 greater than  transitions is xcex94xcexd01inhomo, xcex94xcexdBw preferably be set smaller than a value obtained by subtracting half of xcex94xcexd01inhomo from xcexd01center.
Further, the quantum states of the physical systems as the result of the computation can be read out by irradiating the physical systems with light and detecting the emissions of light from the physical systems. In this case, if the physical systems are irradiated with light resonant with one of the optically allowed two transitions not resonant with the resonator mode while scanning the frequency thereof, the result can be read out without influenced by the physical systems not utilized as the qubit. Note that the result read-out can be performed based on the transmission intensity of light applied to the physical systems.
A quantum information processor according to the present invention comprises: physical systems each having three energy levels, two transitions of three transitions between the three levels being optically allowed, wherein a quantum bit of each physical system is expressed by either of quantum states of two levels constituting a remaining optically forbidden transition or by their superposition state, and wherein at least two physical systems are included, one transition of the optically allowed two transitions being different in transition frequency for respective physical systems; a resonator provided around the physical systems and having a resonator mode that resonates with the other transition of the two transitions of the physical system which are optically allowed; and a light source and an optical system configured to irradiate the physical systems with two kinds of light.
The processor according to the present invention may comprise an electromagnet for applying a magnetic field to the physical systems so as to break degeneracy of levels. In the present invention, it is preferable that the optical system is configured to divide light from the light source into a plurality of optical paths, and that each optical path is provided with an acoustooptic device configured to control a frequency of the light from the light source and an electrooptic device configured to generate light pulse train. In such a configuration, data input, computation operation and result read-out are performed using the optical paths and by irradiating the physical systems with one or two kinds of light having desired frequencies. Further, it is preferable to constitute the light source and the optical system to apply light while scanning the frequency thereof. In addition, it is preferable to provide a photodetector for detecting light emitted from the physical systems due to light irradiation to the physical systems. The result of detection by the photodetector can be converted into electrical signals and recorded.
Additional objects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out hereinafter.